The permeability of the neuronal membrane to different ions determines both resting membrane potential (RMP) and input conductance. These parameters determine the cells response to synaptic input. In this thesis I have examined how the molecular properties of potassium and chloride ion channels can influence neuronal excitability in ways that have not previously been considered. For example, two‐pore domain potassium (K2P) channels open at rest to generate a persistent potassium ion efflux. In addition to its accepted role in setting the RMP, I have tested the hypothesis that this conductance is sufficient to repolarise the membrane during an action potential (AP) in the absence of voltage‐dependent potassium channels (Kv). We tested this prediction using heterologous expression of TASK3 or TREK1 K2P channels combined with conductance injection to simulate the presence of a voltage‐gated sodium conductance. These experiments demonstrated that K2P channels are sufficient to support APs during short and prolonged depolarising current pulses. The membranes permeability to chloride ions can also be affected by extrasynaptic GABAA receptors containing the delta subunit (δ‐GABAARs) that produce a tonic conductance due to their high apparent affinity for GABA. The anaesthetics Propofol and THIP are both believed to alter neuronal excitability by enhancing this persistent chloride flux. We have examined how this anaesthetic action is affected by the steady‐state ambient GABA concentrations that are believed to exist in vivo. Surprisingly, the anaesthetic enhancement of δ‐GABAARs is lost at low ambient GABA concentrations. Therefore, I would suggest that the anaesthetic potency of these drugs is affected by the resting ambient GABA concentration in a manner that has not previously been appreciated. In the current Thesis I have examined the molecular and pharmacological properties of two very different ion channel families that both generate a leak conductance, and I will present models that link the behaviour of these ion channels to their ability to modulate neuronal excitability.